Pressure

Okay, so I'm going to talk about the pressure over here. First off, I want to mention this. I have 23 videos on pressure and the course related to fluid mechanics. Okay, so I will be scratching the surface over here. So, for those of you who are interested in learning more about the pressure, you can go and learn about it in the videos, and I'll put a link over here, okay, to the playlist. Okay, let's go ahead and write the equation. The pressure is equal to force divided by area, right? And you have the surface as an example. You have this point over here, and this is the F, and your pressure will be F divided by A, right? Wrong. Not right. Why? Because I didn't write it well. This is what I'm going to get in the exam, that's for sure. But here is where the mistake is. I need to look at the normal. So it needs to be F N, the normal component. So it needs to be F N divided by A. Okay, so now I have to add this normal force component per applied area. Okay, and we don't really care about pressure too much in solid mechanics courses, but in thermodynamics, fluid mechanics, heat transfer courses, we'll care about it a lot because it changes my, uh, you know, state. Did you realize that pressure is one of the properties, right? So that's why it's very important. And if you want to have a controversy and solve this in the case that you're making some connections, in solid mechanics courses that you're taking, it's like a normal stress, right? I mean, it's obviously there because this is the normal force. Normal force divided by area is normal stress, right? Okay, so let's look at the units. We discussed the units in a separate video, but let's do this. This F A, right? So I have, I'm going to start with SI. One Newton per meter square, and we have a special name for it, Pascal, right? So this is in the SI, right? One thing I want to highlight is if you get, like, you know, 0.7 Pascal or something, I'm almost certain you made a mistake somewhere. Okay, the reason is one pascal is absolutely tiny. We never deal with pascals. We deal with kilopascals. Okay, and let me give you an example. You're now listening to me. I'm assuming that you are at the sea level, and this is how much pressure is applied on your body at this moment in time: 101325. Okay, this is in pascals. So I can simply write it as 101.325 kilopascals. And this is also written as 1.01325 bar. Okay, one bar is 100 kilopascals. You can clearly see from here, right? Now, this is the SI side of it. If you look at the British gravitational side, we use something called psi. This psi is something to really be careful about. Okay, because this psi means pound per square inch. But I'm pretty certain all the other units that will be in the question or, you know, the case that you're dealing with will be in feet. So I have to make sure that I convert properly. Okay, actually, some people call, use psf. It's not the official, you know, unit. But this psf is going to be 144 times psi, and that will be consistent with many of the units that you will be getting. So please be careful about this psi. All right, but regardless of where you're watching this video or which country you're at, you know, an interesting observation, at least when I travel to many different places, is the higher pressure is always measured in psi. Okay, so we mentioned that it is, you know, like 30 psi. For some reason, we use psi, okay? Although you may not realize it. Okay, this is P atm, atmospheric pressure, and you can see over here, this, this, this, this. Whichever you take doesn't matter. Let's say that this is absolute zero. Okay, zero pressure, which is called vacuum, right? We cannot reach that, that's a different story. But let's assume this is the zero pressure. This is the P atm. And let's say that I have a pressure gauge, and I measure my pressure to be, let's say, this line. Okay, and let's assume that that line, and let's use the SI for the time being, is 111.325 kilopascals I measured it, okay? So now, what is the pressure here? That's the question I'm posing to you. What is the pressure? Just like when I did the temperature in the previous segment, I was talking about different Fahrenheit, Kelvin, Rankine, right? So now I have to express myself, and with respect to what? What am I talking about? Okay, so I'm going to introduce to you what I'm talking about. In absolute pressure, and we designate this P abs, the first three letters, right, this is relative to vacuum. Okay, so then you get this, you know, in terms of the number. So if I have this height, will be my P absolute. Okay, the second thing that we may have is the gauge pressure. Okay, P g, P gauge. And this is relative to P atm. So then, if I look here, this will be my P gauge. This will be the P abs. So you can see a clear relationship over here. My P abs will be equal to P gauge plus P atm, right? You can see, you know, like, this is the, you know, sum these two up. P atm, this plus this, is the length of that line, right? So this is a relationship that we need to, you know, know. Okay, um, the thing that we need to be careful about is when I say, you know, I know everybody says to me when I teach face to face, "Oh, I love this. This is great." This is not so much, right? But I'll tell you a counterpoint. Here's my counterpoint. When I say you the pressure is, let's say 111.325 kilopascals, related to what? I mean, to here or to here? There's no distinction because the unit is the same, kilopascal. But what is brilliant about the British gravitational system is that we distinguish it. If it is in, for instance, you may have seen this before: psia means that this is absolute. Do you see, the first letter psi? So there is this Psig in terms of the gauge, okay? So this kind of differentiates this wonderfully for us. So it's much more convenient from that angle. There's this advantage because the advantage is two. So I want you to be cognizant of that, okay? Um, don't get confused. So we need to set the, uh, we need to set the bar here, and we need to talk to each other. And whenever I give you a pressure and I say, you know, like, in this particular case, 111.325 kilopascal, I'm talking about absolute, okay? Unless I specifically tell you that it is P gauge, it is P absolute. I'm not going to repeat myself every single time, okay? So it's going to be P absolute every time I mention a pressure value. If I'm solving a question from British gravitational, I don't have to worry about it. I will be much more specific. I can be much more specific, okay? Another thing that, you know, the books does, including the textbook that I use, is something called the vacuum. I absolutely don't like it at all, and I don't use it, but I want to, you know, show in case, you know, it's, it's, it's your stuff. So the way that I use the gauge pressure is the gauge pressure can be negative, okay? So you can see the gauge pressure can go down. So what, you know, some of the resources call it, this P vacuum is what they call, but then it gets confused with this. That's why I don't like it, okay? So, you know, just note that if it is negative, uh, Pg turns out to be a negative value. They call it P vacuum, right? So that is, uh, you know, an important distinction. Okay, now, now I know my how to communicate, respect the pressures. I know what a pressure is. Now let's talk about how the pressure varies with depth, okay? I said that I will not cover stuff a lot because the fluid mechanics class will pick it up from here, but this is something that I really need in this particular class with that, okay? Um, so for gases; in thermo, for the common applications that we'll be dealing with, the pressure variation with respect to height is negligible because most of the, you know, I gave you the, uh, you know, in the video 1.1, thermo 1.1, I gave you a bunch of different applications. All of them, the variation of height was negligible, okay? So the pressure does not change in terms of height. Um, please forget what I just said if you're taking the fluid mechanics class. In that one, we are dealing with airplanes, right? Then you, you cannot simply neglect the pressure variation, okay? So that's a different, uh, ball game. But this particular class, we are gonna neglect this, right? Which is a good assumption for the application space. For liquids, you cannot, unfortunately, do the same, you know, assumption, okay? And I actually, you know, I derive this in the fluid mechanics class. I'm not going to do it over here, but I'm assuming z is pointing up over here. So let's say this is the, actually, let's do a good job, or it's called a better job, because I don't know if I can do better, you know, a good job. But anyways, so this is the free surface, and we designate it with an upside-down triangle, okay? And the z is pointing up here like this. x is this way. y is into the page. z is pointing up. In this case, when del P del z, the, the change of pressure in the z direction will be rho g, okay? Negative of rho g. So as I go down, I increase the pressure by amount of rho g, okay? That's why when you're diving in the St. Pete beach, as an example, you will feel more pressure in your ears because it's directly proportional to how much you go down. If the pressure over here is, let's say, 100, and you go one unit down, 101, 102, 103, 104, 105, whatever, okay? So it just, uh, you know, is linearly proportional. So that's kind of simple. Obviously, in this case, I'm assuming a constant density liquid over here, okay? If the liquid is a variable density, then you have to solve this particular equation, which is beyond the scope of this particular class, okay? Um, so I actually can rewrite this in this manner, a little bit better this way. Then I, let's say that I have a point one over here, and I have a point two over here. My P2 will be equal to P1 plus rho g times h, and h is the distance between here and here, right? Like this. So h is that height. So P2 will be more than P1 by the difference will be rho g times h, okay? And you can check it. The units will match as well. We talk about, um, the units on the right-hand side and the left-hand side must match. And in order for me to add to this is Pascal, this needs to be Pascal too. So you can check it yourself, okay? But interesting observation also is del P del z, excuse me, del P del x, will be equal to del P del y will be equal to zero. So there will be no variation of the pressure if I go in this direction or in or out of the page, okay? This direction or this direction, it is not changing. As I go down over here, it's going to increase by rho g h, okay? Um, okay, so let me give you an example. Let me do something. Let me do this. Actually, why don't I draw this, and I'll be right back? Okay, I'm back. So here is the question I'm posing to you now. Where's the relationship between P1, P2, P3? You can see clearly here that this is the smallest area. This is the middle area in terms of the, you know, size of it, and this is the biggest area. So that's my question to you: What is the relation between P1, P2, and P3? Okay, if, for those of you who said this, you are right. So these three pressures will be the same because it's from here, right? So you can have this, this value to be common because the height of the fluid is the same. So this P1 may be aligned with that, and the P2 here, it will be right over here, right over here, right over here. h is the same, so rho is the same. It's the same liquid that I'm dealing with. The gravity doesn't change, and the h is the same. So you can see the pressures will be the same at the bottom, bottom of the tank, okay? What about the forces, okay? How about the F1, F2, F3? Force is equal to P A, right? So P is the same. So this will be basically, the area will be the name of the game, right? The bigger the area, the bigger the force. So you can see over here that I'm going to get myself F3 will be larger than F1 will be larger than F2, okay? And one more topic I want to add kind of fast over here. Let's say that I have a container like this, one, two, and three. Oh, come on. That's okay, I guess. This is like that, and let's say that I have another interface over here, I have another interface over here, I have another interface over here, and let's say that I'm calculating this P, okay? So let's call this h A, h B, h C, h D, in terms of the heights of these each liquid is different from one another, okay? So that P that I'm interested in will be equal to P atm. I'm assuming this is open to the atmosphere right over here plus rho A g h A plus rho B g h B plus rho C g h C plus rho D g times h D, okay? So that will be the pressure. So you simply add them up, okay? There's also something called the manometers. I will link a video here because I don't want to cover it. I already have extensive coverage on that one, okay? All right, so this is gonna end of first module. I'll come back with the second module soon. Thank you for watching this video as well. Take care.